I would first contact him in a nonconfrontational way: email, text message, or some other method where he doesn't have to immediately respond or worry that you're going to scold him again. Say something like, "I want to apologize; can we talk?" Offer circumstances as if you were setting a date or a meeting: "We can get coffee on Thursday or Friday" or even "I can meet you outside the dining hall after Biology."
When you meet: admit fault, say how you feel, clearly apologize, and request forgiveness. An example might be, "I misunderstood something and scolded you. Now I feel embarrassed. I'm sorry for doing that. Can we put it behind us?"
It'll be a difficult conversation to have. He might not accept your apology or be willing to forgive you. If he doesn't, that's fine. You can't force him to overlook your mistake.